1. Field of the Invention
The present invention relates to a movement trajectory generating method of a dynamical system. More specifically, the present invention relates to a movement trajectory generating method of a dynamical system, which is capable of automatically generating, by least dissipation of energy, an objective trajectory of a dynamical system having nonlinear characteristics such as robots, power generation plants, motor engines, elevators, trains, cars and other vehicles, and which makes it possible to speech synthesis or to recognize continuous speech.
2. Description of the Background Art
Conventionally, teaching of a trajectory of an articulated industrial manipulator or the like is determined by a human operator in an on-line manner in a manufacturing line of a factory. However, since the manufacturing line is in operation during the daytime, teaching can be conducted only at night or on holidays. In addition, such conventional teaching method has difficulties in view of limited resources such as lack of skilled workers. Therefore, off-line trajectory generating techniques are desired. Although such off-line trajectory generating techniques are still under study, several computing geometrical methods have been proposed as solutions of problems for defining a trajectory in a minimum course while avoiding obstacles in a three-dimensional space by taking no account of the dynamics of the controlled object.
However, according to such methods, the calculation time is exponentially increased when the degrees of freedom of the controlled object and the number of obstacles are increased, and therefore such methods are not practical. In addition, since the dynamics of the controlled object is not taken into account in such methods, smooth movement cannot be obtained and excessive load is applied to the controlled object.
On the other hand, conventional optimum control methods for obtaining the optimum trajectory by setting a certain evaluation function taking account of the dynamics, strict modeling of a controlled object is indispensable for numerical calculation.
However, it is practically impossible to obtain strict modeling due to interference between articulations of a dynamical system such as an articulated industrial manipulator or due to nonlinearity of motors or speed reducing mechanisms. Thus, systematic methods for automatically forming a trajectory of a nonlinear controlled object moving smoothly and avoiding a large number of obstacles are not proposed in the prior art.